MATH137 Lecture Notes - Lecture 11: Riemann Sum, Antiderivative, Power Rule

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Catherine Briggs

Document Summary

Math 137 week 11 notes dr. paula smith. 4. 9 we know how to take the derivative of several families of functions. E. g. , the derivative of sin x is cos x. Now we wish to work backward: given cos x, is there a function such that the derivative of that function is cos x. Clearly the answer is yes: sin x is such a function. However, so is sin x + c, where c is any real number. Function f is called an antiderivative of function f on interval i if f (x) The most general antiderivative of f on interval i is. F(x) + c, where c is an arbitrary constant. Hence differentiation and taking an antiderivative are almost inverse operations. They are not quite so, because, though the derivative of the antiderivative of f(x) is f(x), the antiderivative of the derivative of f(x) is f(x) + c.